Question: William is 24 years older than Umaima. Nine years ago, William was 4 times as old as Umaima. How old is Umaima now?
Explanation: We can use the given information to write down two equations that describe the ages of William and Umaima. Let William's current age be $w$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $w = u + 24$ Nine years ago, William was $w - 9$ years old, and Umaima was $u - 9$ years old. The information in the second sentence can be expressed in the following equation: $w - 9 = 4(u - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = u + 24$ . Substituting this into our second equation, we get the equation: $(u + 24)$ $-$ $9 = 4(u - 9)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 15 = 4 u - 36$ Solving for $u$ , we get: $3 u = 51$ $u = 17$.